The Big Apple - where originated this expression?

Why Big Apple?

There exist several explanations but it cannot be agreed upon a particular one among diverse scenes - anyhow one explanation became the official version.

Most of the stories around the phrase 'big apple' have to do with the earning of money in NYC.

The phrase was documented for the the first time in Edward S. Martin's book 'The Wayfarer in New York', published 1909, when he used 'Big Apple' as a metaphor for New York City. In this metaphor sense New York is the fruit, the 'big' apple, of a tree which has roots reaching down into the Mississippi valley and branches spanning from ocean to ocean. That means that this tree gets its strength, potency from far away, from where people flock to the city to make their luck, to improve their business, to find, receive the bigger fruits (in this context: apples). In a nutshell: it was said that efforts paid off much better there.

No doubt about it: New York City had the right potency, the city's growth was immense and capital accumulated real quick.

So far so good. But what about other theories? Or were they just inherited from Martin's statement. Even if he was the one laying the cornerstone of this now famous metaphor, it may be doubted that his book gained such broad reach to establish a well-known phrase.

At this point another theory and a man named Mr. John F. FitzGerald come into play: On February 18th, 1924, this well-renowned sport reporter and columnist (he actually wrote about horse racing) originated a new column in the New York Morning Telegraph, for which he worked. The name of the column was: "Around the Big Apple", supported by an illustration showing an outlined apple with - apparently - the New York City skyline in it.
And he explained as following: "The Big Apple. The dream of every lad that ever threw a leg over a thoroughbred and the goal of all horsemen. There's only one Big Apple. That's New York." 
As he later explained, he overheard a conversation between to stable hands, who referred to New City as the 'Big Apple', the city where a man - and of course in company of his Thoroughbred - could make the real big money.
This story is meanwhile the official one of the City of New York and was discovered eventually by Mr. Barry Popik, a word historian and law judge with New York City's Bureau of Parking Violations. Additionally he convinced city representatives to rename the corner Broadway and W 54th St, where FitzGerald lived from 1934 on for 29 years, to 'Big Apple Corner'.

In the 70' New York City's Tourism Directors chose the red Big Apple logo and the phrase 'The Big Apple' as their distinctive mark.

Before the 'FitzGerald' explanation evolved to be the official one, it was believed that the phrase originated in the 1930s, when it was heavily used by black Jazz musicians. They called a well paid gig in New York a 'Big Apple'. Again: a metaphor for making the big money. Basically they used the expression in the same way as Edward S. Martin did. There were many apples on the tree of success but the real big one is the gig in New York.
At this time New York was the ultimate 'new' spot for Jazz musicians and the place where having a good gig could have meant a breakthrough!
Evidence or not: there was even a Harlem Jazz Club named: Big Apple. Anyhow, the connection between 'Big Apple' and the Jazz Scene can be seen, but as said, it's not the official side of the story of 'The Big Apple'.